首次为数据估值提供误差与收敛性分析，确保单次训练中估值有效性。
Error Estimate and Convergence Analysis for Data Valuation
- 基于神经动力学框架，建立损失差值的二次误差界。
- 证明训练损失梯度范数渐近为零，元损失亚线性收敛。
- 适用于需可靠数据重要性评估的研究者，如模型调试与数据清洗。
数据估值用于衡量数据的重要性，但现有方法无法保证单次训练过程中的有效性。神经动力学数据估值（NDDV）方法[3]解决了这一局限。本文首次针对NDDV开展误差估计与收敛性分析。在Lipschitz与光滑性假设下，我们推导出损失差值的二次误差界，其随时间步数倒数递减，且与控制变量变化的平方成正比，保证了稳定性。同时证明训练损失的期望平方梯度范数渐近趋于零，元损失随迭代次数亚线性收敛。特别地，NDDV实现亚线性收敛。
原文摘要 · Abstract (English)
Data valuation quantifies data importance, but existing methods cannot ensure validity in a single training process. The neural dynamic data valuation (NDDV) method [3] addresses this limitation. Based on NDDV, we are the first to explore error estimation and convergence analysis in data valuation. Under Lipschitz and smoothness assumptions, we derive quadratic error bounds for loss differences that scale inversely with time steps and quadratically with control variations, ensuring stability. We also prove that the expected squared gradient norm for the training loss vanishes asymptotically, and that the meta loss converges sublinearly over iterations. In particular, NDDV achieves sublinear convergence.
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